The proposal, aired at a packed public hearing Monday at City Hall, would increase the amount of relocation money that landlords must pay to certain tenants who are evicted and, with a few exceptions, prohibit landlords from taking away storage, parking and yards from tenants without their consent.

It also would put residential hotel rooms under the city's rent control protections and restrict a landlord's ability to limit the number of people living in a rental unit.

Tenants groups, including the San Francisco Tenants Union and the Eviction Defense Collaboration, say the law needs to be strengthened to even the playing field for tenants and landlords. Some of the provisions in Gonzalez's package, they say, would simply codify what already is the policy of the San Francisco Rent Board.

Ted Gullicksen of the tenants union said some landlords had evicted tenants who marry, on the grounds that the lease allows only one tenant. He wants the law changed to mirror the city's legal occupancy levels outlined in the housing code.

But Brook Turner of the Coalition for Better Housing said that could result in a half-dozen people or more being allowed to live in a 500-square- foot studio apartment. He said that he doesn't condone evicting someone who gets married, but he added that Gonzalez's proposal would go too far in trying to remedy the problem.

Gonzalez called his proposal "a starting point, a general framing of the issue." He said that he was open to compromise and that he expected Monday's hearing to be the first of many to discuss his proposal.

San Francisco's rent control law, more than 20 years old, is one of the toughest in the nation and reflects a city in which two-thirds of the residents rent. Tenants and landlords have been fighting for years over the issue, sparring at City Hall, at the ballot and in court.

Among other aspects of the Gonzalez bill:

-- New landlords could be liable for illegal rent increases imposed under former owners.

-- So-called banked rent increases would be limited. By law, landlords can save up annual allowable rent hikes -- this year's is 0.8 percent -- and impose them all at once. Gonzalez would force landlords to spread out the increase and limit the increase in any one year to 8 percent.

-- Relocation fees paid by landlords would be increased $500, to $2,000 for each person displaced by an owner move-in eviction. For evictions for capital improvements in which a tenant is forced out while the apartment is fixed up, landlords' fees would double to $2,000. And for the first time, landlords whose units are demolished -- which happens mostly in cases of illegal construction -- would owe relocation fees.

-- Landlords would have to act "in good faith and without ulterior motive" in evicting a tenant, even if it's for good cause, such as in cases where tenants aren't paying rent or are dealing drugs out of an apartment.

-- Rent control would be extended to renters' secondary homes. Currently, rent control is not imposed on a person's nonprimary residence.